Joe owns a small factory and the supplier of raw materials offers him the following deal: if he orders less than or equal to 30k units, the unit price is $0.7. If he the order is more than 30k but less than or equal to 50k units, the unit price is S0.6. If the order is more than 50k but less than or equal to 100k units, the unit price is $0.4. If the order is more than 100k, the unit price is $0.3. Joe cannot store more than 120k units in his warehouse. Develop the mixed integer programming formulation to minimize the purchase cost. Clearly define your decision variable(s), write down the objective function and constraints. (15 points)